{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-09-01T08:15:12.813685Z",
     "start_time": "2025-09-01T08:15:12.383182Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-01T08:15:12.818265Z",
     "start_time": "2025-09-01T08:15:12.813685Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#定义目标函数\n",
    "def f(x):\n",
    "    return x**2\n",
    "#定义梯度函数(导函数)\n",
    "def gradient(x):\n",
    "    return 2*x\n"
   ],
   "id": "8452eba00f78c7cd",
   "outputs": [],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-01T08:15:12.823305Z",
     "start_time": "2025-09-01T08:15:12.818265Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#用列表保存点的变化轨迹\n",
    "x_list = []\n",
    "y_list = []"
   ],
   "id": "3bdaf27f3489d997",
   "outputs": [],
   "execution_count": 3
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-01T08:15:12.828050Z",
     "start_time": "2025-09-01T08:15:12.823305Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#定义超参数和x的初始值\n",
    "alpha = 0.1\n",
    "x = 1"
   ],
   "id": "db3c1e5e6a001085",
   "outputs": [],
   "execution_count": 4
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-01T08:15:39.164959Z",
     "start_time": "2025-09-01T08:15:39.158700Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 重复迭代100次\n",
    "for i in range(100):\n",
    "    y = f(x)\n",
    "    #记录当前点的坐标\n",
    "    x_list.append(x)\n",
    "    y_list.append(y)\n",
    "    print(f\"x={x}, f(x)={y}\")\n",
    "    #计算梯度\n",
    "    grad = gradient(x)\n",
    "    #更新参数\n",
    "    x = x - alpha*grad"
   ],
   "id": "74c842bc6e2279fd",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=1, f(x)=1\n",
      "x=0.8, f(x)=0.6400000000000001\n",
      "x=0.64, f(x)=0.4096\n",
      "x=0.512, f(x)=0.262144\n",
      "x=0.4096, f(x)=0.16777216\n",
      "x=0.32768, f(x)=0.10737418240000002\n",
      "x=0.26214400000000004, f(x)=0.06871947673600003\n",
      "x=0.20971520000000005, f(x)=0.04398046511104002\n",
      "x=0.16777216000000003, f(x)=0.02814749767106561\n",
      "x=0.13421772800000004, f(x)=0.018014398509481992\n",
      "x=0.10737418240000003, f(x)=0.011529215046068476\n",
      "x=0.08589934592000002, f(x)=0.0073786976294838245\n",
      "x=0.06871947673600001, f(x)=0.004722366482869647\n",
      "x=0.05497558138880001, f(x)=0.003022314549036574\n",
      "x=0.04398046511104001, f(x)=0.0019342813113834073\n",
      "x=0.035184372088832, f(x)=0.0012379400392853804\n",
      "x=0.028147497671065603, f(x)=0.0007922816251426435\n",
      "x=0.02251799813685248, f(x)=0.0005070602400912918\n",
      "x=0.018014398509481985, f(x)=0.00032451855365842676\n",
      "x=0.014411518807585589, f(x)=0.00020769187434139315\n",
      "x=0.01152921504606847, f(x)=0.0001329227995784916\n",
      "x=0.009223372036854777, f(x)=8.507059173023463e-05\n",
      "x=0.007378697629483821, f(x)=5.444517870735016e-05\n",
      "x=0.005902958103587057, f(x)=3.4844914372704106e-05\n",
      "x=0.004722366482869646, f(x)=2.230074519853063e-05\n",
      "x=0.0037778931862957168, f(x)=1.4272476927059604e-05\n",
      "x=0.0030223145490365735, f(x)=9.134385233318147e-06\n",
      "x=0.002417851639229259, f(x)=5.846006549323614e-06\n",
      "x=0.001934281311383407, f(x)=3.741444191567113e-06\n",
      "x=0.0015474250491067257, f(x)=2.3945242826029522e-06\n",
      "x=0.0012379400392853806, f(x)=1.5324955408658897e-06\n",
      "x=0.0009903520314283045, f(x)=9.807971461541695e-07\n",
      "x=0.0007922816251426436, f(x)=6.277101735386685e-07\n",
      "x=0.000633825300114115, f(x)=4.017345110647479e-07\n",
      "x=0.0005070602400912919, f(x)=2.571100870814386e-07\n",
      "x=0.0004056481920730336, f(x)=1.6455045573212074e-07\n",
      "x=0.00032451855365842687, f(x)=1.0531229166855728e-07\n",
      "x=0.0002596148429267415, f(x)=6.739986666787666e-08\n",
      "x=0.0002076918743413932, f(x)=4.313591466744107e-08\n",
      "x=0.00016615349947311455, f(x)=2.7606985387162278e-08\n",
      "x=0.00013292279957849163, f(x)=1.7668470647783856e-08\n",
      "x=0.00010633823966279331, f(x)=1.130782121458167e-08\n",
      "x=8.507059173023465e-05, f(x)=7.2370055773322674e-09\n",
      "x=6.805647338418771e-05, f(x)=4.631683569492651e-09\n",
      "x=5.444517870735017e-05, f(x)=2.9642774844752965e-09\n",
      "x=4.3556142965880136e-05, f(x)=1.8971375900641898e-09\n",
      "x=3.4844914372704106e-05, f(x)=1.2141680576410813e-09\n",
      "x=2.7875931498163285e-05, f(x)=7.77067556890292e-10\n",
      "x=2.230074519853063e-05, f(x)=4.973232364097869e-10\n",
      "x=1.7840596158824504e-05, f(x)=3.1828687130226364e-10\n",
      "x=1.4272476927059604e-05, f(x)=2.0370359763344877e-10\n",
      "x=1.1417981541647683e-05, f(x)=1.3037030248540718e-10\n",
      "x=9.134385233318147e-06, f(x)=8.343699359066061e-11\n",
      "x=7.307508186654517e-06, f(x)=5.3399675898022794e-11\n",
      "x=5.8460065493236135e-06, f(x)=3.417579257473458e-11\n",
      "x=4.676805239458891e-06, f(x)=2.1872507247830133e-11\n",
      "x=3.741444191567113e-06, f(x)=1.3998404638611287e-11\n",
      "x=2.9931553532536903e-06, f(x)=8.958978968711224e-12\n",
      "x=2.3945242826029522e-06, f(x)=5.733746539975183e-12\n",
      "x=1.915619426082362e-06, f(x)=3.669597785584118e-12\n",
      "x=1.5324955408658897e-06, f(x)=2.3485425827738356e-12\n",
      "x=1.2259964326927118e-06, f(x)=1.503067252975255e-12\n",
      "x=9.807971461541693e-07, f(x)=9.61963041904163e-13\n",
      "x=7.846377169233355e-07, f(x)=6.156563468186643e-13\n",
      "x=6.277101735386684e-07, f(x)=3.9402006196394517e-13\n",
      "x=5.021681388309347e-07, f(x)=2.5217283965692494e-13\n",
      "x=4.0173451106474777e-07, f(x)=1.6139061738043196e-13\n",
      "x=3.213876088517982e-07, f(x)=1.0328999512347644e-13\n",
      "x=2.5711008708143857e-07, f(x)=6.610559687902492e-14\n",
      "x=2.0568806966515085e-07, f(x)=4.230758200257595e-14\n",
      "x=1.6455045573212068e-07, f(x)=2.7076852481648607e-14\n",
      "x=1.3164036458569655e-07, f(x)=1.732918558825511e-14\n",
      "x=1.0531229166855724e-07, f(x)=1.109067877648327e-14\n",
      "x=8.424983333484579e-08, f(x)=7.0980344169492925e-15\n",
      "x=6.739986666787664e-08, f(x)=4.542742026847548e-15\n",
      "x=5.391989333430131e-08, f(x)=2.9073548971824307e-15\n",
      "x=4.313591466744105e-08, f(x)=1.8607071341967557e-15\n",
      "x=3.4508731733952836e-08, f(x)=1.1908525658859235e-15\n",
      "x=2.760698538716227e-08, f(x)=7.62145642166991e-16\n",
      "x=2.2085588309729814e-08, f(x)=4.877732109868742e-16\n",
      "x=1.7668470647783853e-08, f(x)=3.1217485503159956e-16\n",
      "x=1.4134776518227082e-08, f(x)=1.9979190722022372e-16\n",
      "x=1.1307821214581666e-08, f(x)=1.2786682062094318e-16\n",
      "x=9.046256971665333e-09, f(x)=8.183476519740364e-17\n",
      "x=7.237005577332267e-09, f(x)=5.2374249726338334e-17\n",
      "x=5.789604461865813e-09, f(x)=3.351951982485653e-17\n",
      "x=4.631683569492651e-09, f(x)=2.145249268790818e-17\n",
      "x=3.7053468555941204e-09, f(x)=1.3729595320261235e-17\n",
      "x=2.9642774844752965e-09, f(x)=8.786941004967191e-18\n",
      "x=2.371421987580237e-09, f(x)=5.623642243179002e-18\n",
      "x=1.8971375900641898e-09, f(x)=3.599131035634562e-18\n",
      "x=1.517710072051352e-09, f(x)=2.3034438628061197e-18\n",
      "x=1.2141680576410815e-09, f(x)=1.4742040721959166e-18\n",
      "x=9.713344461128653e-10, f(x)=9.434906062053868e-19\n",
      "x=7.770675568902922e-10, f(x)=6.0383398797144755e-19\n",
      "x=6.216540455122338e-10, f(x)=3.8645375230172647e-19\n",
      "x=4.97323236409787e-10, f(x)=2.473304014731049e-19\n",
      "x=3.978585891278296e-10, f(x)=1.5829145694278712e-19\n",
      "x=3.182868713022637e-10, f(x)=1.0130653244338377e-19\n",
      "x=2.5462949704181097e-10, f(x)=6.483618076376562e-20\n"
     ]
    }
   ],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-01T08:17:28.453086Z",
     "start_time": "2025-09-01T08:17:28.328338Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#画图\n",
    "x = np.arange(-1,1,0.01)\n",
    "plt.plot(x,f(x))\n",
    "plt.plot(x_list,y_list,\"r\")\n",
    "plt.scatter(x_list,y_list,color=\"r\")"
   ],
   "id": "9d5f55738eae5703",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1b8ef153aa0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "eb3df5e137f174e2"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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